| Planar cell polarity (PCP) signaling refers to the coordinated polarization of cells within the plane of various epithelial tissues to generate sub-cellular asymmetry along an axis orthogonal to their apical-basal axes. For example, in the Drosophila wing, PCP is seen in the parallel orientation of hairs that protrude from each of the approximately 30,000 epithelial cells to robustly point toward the wing tip. Through a poorly understood mechanism, cell clones mutant for some PCP signaling components, including some, but not all alleles of the receptor frizzled, cause polarity disruptions of neighboring, wild-type cells, a phenomenon referred to as domineering nonautonomy. Previous models have proposed diffusible factors to explain nonautonomy, but no such factors have yet been found.; This dissertation describes the mathematical modeling of PCP in the Drosophila wing, based on a contact dependent signaling hypothesis derived from experimental results. Intuition alone is insufficient to deduce that this hypothesis, which relies on a local feedback loop acting at the cell membrane, underlies the complex patterns observed in large fields of cells containing mutant clones, and others have argued that it cannot account for observed phenotypes. Through reaction-diffusion, partial differential equation modeling and simulation, the feedback loop is shown to fully reproduce PCP phenotypes, including domineering nonautonomy. The sufficiency of this model and the experimental validation of model predictions argue that previously proposed diffusible factors need not be invoked to explain PCP signaling and reveal how specific protein-protein interactions lead to autonomy or domineering nonautonomy.; Based on these results, an ordinary differential equation model is derived to study the relationship of the feedback loop with upstream signaling components. The cadherin Fat transduces a cue to the local feedback loop, biasing the polarity direction of each cell toward the wing tip. The feedback loop then amplifies and propagates PCP across the pupal wing, but polarity information does not always propagate correctly across cells lacking Fat function. Using the simplified model, the presence and severity of polarity defects in fat clones is shown to be an inherent consequence of the feedback loop when confronted with irregular variations in cell geometry. |
